From reading a book on NASA's Voyager mission, I learned that before the launch of these spacecraft, the expectation was that the heliopause was at around Jupiter or Saturn's orbit which is about 5 to 10 AU. The book says that as the spacecraft continued to move away from the sun, the space physicists kept increasing their estimate of the position of the heliopause. If it's about an energy or flux balance, then the estimate would be defined by a certain area of the sphere where the heliopause occurs, and since areas are proportional to the square of the radius they got the number wrong by as much as $(100/5)^2 = 400$. That's a huge underestimate of the sun's output or a huge overestimate of what goes on in interstellar space.

The book doesn't explain why it is that early estimates were wrong and I didn't see an explanation. Perhaps someone knows and will give a nice intuitive explanation for the estimates.

So as of 1959, by direct experimental observation, it was known that the heliopause was at least the radius of the earth or R⊙.

Pneuman and Kopp 1971 Model: According
to a more complex but still simplified
MHD [MagnetoHydroDynamics] model of the coronal structure
(ISP p. 114-117 etc., the model of
Pneuman and Kopp 1971), the dipolar
magnetic field lines form closed loops
if they originate at solar latitudes
of less than about 45° (above or below
the solar equator). However, those
arising greater than about 45° are
open field lines that may curve around
the closed region to some extent but
eventually extend far into space in
all directions, at least beyond a
heliocentric distance of about 2 R⊙.

This is the only paper I've been able to find that approximately reads on the magnetopause question. This is a highly cited paper and it's early enough to influence the expectations at the Voyager launches (1977). So I believe that the Pneuman and Kopp paper gave the expectation that the heliopaue would be at around 2 R⊙ based on MHD calculations. Since this was a huge error, I've not been able to find any better detail.

The man who developed MHD was Hannes Alfvén. He got the 1970 Nobel prize in physics for this. His Nobel prize lecture was partially dedicated to the task of claiming that his theory was being abused. In particular, he noted that the space physics situation was out of control. From his lecture, I've italicized the parts having to do with space physics predictions:

Plasma physics, space research and the origin of the solar system
[ Nobel Prize Lecture, 1970, by Hannes Alfvén ]

... The cosmical plasma physics of
today is far less advanced than the
thermonuclear research physics. It is
to some extent the playground of
theoreticians who have never seen a
plasma in a laboratory. Many of them
still believe in formulae which we
know from laboratory experiments to be
wrong. The astrophysical
correspondence to the thermonuclear
crisis has not yet come. The reason
for this is that several of the basic
concepts on which the theories are
founded, are not applicable to the
condition prevailing in cosmos. They
are "generally accepted" by most
theoreticians, they are developed with
the most sophisticated mathematical
methods and it is only the plasma
itself which does not "understand",
how beautiful the theories are and
absolutely refuses to obey them. It is
now obvious that we have to start a
second approach from widely different
starting points.

If you ask where the border goes
between the first approach and the
second approach today, an approximate
answer is that it is given by the
reach of spacecrafts. This means that
in every region where it is possible
to explore the state of the plasma by
magnetometers, electric field probes
and particle analyzers, we find that
in spite of all their elegance, the
first approach theories have very
little to do with reality. It seems
that the change from the first
approach to the second approach is the
astrophysical correspondence to the
thermonuclear crisis. ...

The above lecture includes a table with a detailed comparison between the "first approach" and "second approach".

Conclusion:

The problem in estimating the heliopause was mostly due to theoreticians overestimating their understanding of the limitations of MHD. In particular, the MHD equations fail when electric currents are strong enough to overcome the magnetic field. This breaks the MHD assumption that ions and electrons remain pinned to magnetic field lines.

There was a considerable stretch when getting answers to within an order of magnitude was pretty good on topics like stellar structure and cosmology. Things improved---first slowly but later on quite markedly---so that now we are in the age of "precision cosmology" (a loss in terms of jokes about putting the error bar on the exponents, alas). But individual topics might have languished if they didn't attract much attention.

This was helpful, but in order to estimate the size as "Jupiter's orbit" surely they must have done a calculation. They put some numbers in and something went wrong.
–
Carl BrannenJan 27 '11 at 2:38

@Carl: You're looking at a calculation involving the solar wind and magnetic fields on one hand and galactic particle flows and magnetic fields on the other. Lots of magnetohydrodynamics, therefore non-linearities. Hard problem, and if any of your inputs are shaky...
–
dmckee♦Jan 27 '11 at 3:40

In any case, they started developing the Voyager spacecraft in the 1960's. The first measurement that a solar wind even existed wasn't reported until 1960-1961 [K. Gringauz using the Lunik 2 spacecraft]. They were able to determine a flux of particles (i.e., number per area per time), but did not determine speed or number density.

Biermann's hypothesis of the existence of the solar wind was between 1951-1957, thus, not much earlier. Though he did approximate the solar wind speed pretty closely with $\sim$500-1000 km/s, which would now be considered fast solar wind.

Mariner 2 was the first spacecraft to show that the solar wind was continuously emitted by the sun (observations and papers between 1962-1967). This is also the period when they first started to get semi-reliable estimates of the bulk flow speed, number density, temperature (i.e., Avg. kinetic energy in the bulk flow rest frame), etc. of the solar wind.

Once these parameters were found, and assuming that dynamic pressure $\propto$ $r^{-2}$ (assume V $\sim$ constant and adiabatic expansion, then n $\propto$ $r^{-2}$), the heliopause can be estimated using the dynamic pressure at 1 AU, $P_{1AU}$, combined with estimates of the interstellar pressure, $P_{I}$, to approximate a standoff distance, $R_{S}$.

If we use the following typical values n $\sim$ 5 $cm^{-3}$ and V $\sim$ 400 km/s, and $P_{I}$ $\sim$ 10$^{-13}$ Pa, then $R_{S}$ $\sim$ 100 AU. So MHD is not required, you can just use simple hydrodynamics to get a rough estimate. If the early estimates of $P_{I}$ were much higher or $P_{1AU}$ much lower, it is reasonable to understand why early estimates of $R_{S}$ may have been grossly inaccurate.

Remember, people weren't even comfortable with whether a solar wind existed until the 1950's. Paul Kellogg predicted the existence of the Earth's bow shock in 1962, which was controversial at the time due to the extremely low collision rates of tenuous plasmas and uncertainties about relevant speeds to use for Mach numbers.

My point is that it was only very recently that we had any measurements of the sun's atmosphere (technically, everything within the heliosphere is considered within the sun's atmosphere). At the time when Voyager was first starting to be discussed and designed, all of this stuff was less than a decade old. It wasn't even until the 1950's that we had a definitive estimate the age of the sun and solar system [e.g., Burbidge et al., 1957].